Demand, Supply, Elasticities (PED, YED, XED, PES), Total Revenue & Tax Incidence

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Demand, Supply, Consumer Surplus & Producer Surplus

A movement along a demand or supply curve (an extension or contraction) is caused solely by a change in the good's own price. A shift of the entire curve is caused by non-price determinants: for Demand (PIRATES: Population, Income, Related goods' prices, Advertising/tastes, Expectations, Seasons); for Supply (PINTSWC: Productivity, Indirect taxes, Number of firms, Technology, Subsidies, Weather, Costs of production). The price mechanism allocates scarce resources via three functions (Adam Smith's 'invisible hand'): SIGNALLING (rising prices signal scarcity), incentive (higher prices incentivize firms to expand output for higher profit), and rationing (rising prices ration scarce goods to those most able and willing to pay). Consumer Surplus is the area below the demand curve and above the market equilibrium price P*; Producer Surplus is the area above the supply curve and below P*.

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2

Price Elasticity of Demand (PED) & Total Revenue

PED measures the responsiveness of quantity demanded of a good to a change in its own price: PED = (%ΔQd) ÷ (%ΔP). Because of the law of downward-sloping demand, PED is almost always negative: |PED| > 1: Price elastic (quantity changes by a larger percentage than price). 0 < |PED| < 1: Price inelastic (quantity changes by a smaller percentage than price). |PED| = 1: UNITARY elastic (rectangular hyperbola where Total Revenue is constant). PED = 0: Perfectly inelastic (vertical demand curve). PED = ∞: Perfectly elastic (horizontal demand curve). Determinants of PED (SPLAT): Substitutes (number and closeness, the most important determinant), Percentage of income spent, Luxury vs necessity, Addictiveness/habit-forming, and Time period. Link to Total Revenue (TR = P × Q): 1. When demand is price inelastic (|PED| < 1), price and Total Revenue move in the same direction (raising price increases TR; cutting price reduces TR). 2. When demand is price elastic (|PED| > 1), price and Total Revenue move in opposite directions (cutting price increases TR; raising price reduces TR). Along any downward-sloping linear demand curve, PED varies from -∞ at the top price-axis intercept, to -1 at the midpoint (where MR = 0 and Total Revenue is maximised), to 0 at the bottom quantity-axis intercept.

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3

Income Elasticity of Demand (YED) & The Trade Cycle

YED measures the responsiveness of quantity demanded to a change in real consumer income: YED = (%ΔQd) ÷ (%ΔY). Here the sign (+ or -) is essential: 1. Normal goods have a positive YED (YED > 0 - as real income rises, demand increases): Normal Necessities (0 < YED < +1, income inelastic): e.g., fresh milk, basic clothing, staple utilities. Luxury / Superior Goods (YED > +1, income elastic): e.g., international business-class flights, designer watches, fine dining. 2. Inferior goods have a negative YED (YED < 0 - as real income rises, consumers switch away to better-quality brands so demand falls; during a recession when real incomes fall, demand for inferior goods like supermarket value-range noodles or bus travel rises). Firms use YED to diversify product portfolios across the macroeconomic business cycle (selling both luxury and counter-cyclical inferior goods).

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4

Cross Elasticity of Demand (XED): Substitutes vs Complements

XED measures the responsiveness of quantity demanded of Good A to a change in the price of another Good B: XED_AB = (%ΔQd of Good A) ÷ (%ΔP of Good B). Again, the sign (+ or -) tells you the relationship between the two goods: 1. Substitutes (competitive demand) have a positive XED (XED > 0): an increase in the price of Good B (e.g., Coca-Cola) causes consumers to switch to Good A (Pepsi), increasing Qd of Good A. Close substitutes have a high positive XED (> +1), while weak substitutes have a small positive XED (0 < XED < +1). 2. Complements (joint demand) have a negative XED (XED < 0): an increase in the price of Good B (e.g., inkjet printers or cinema tickets) reduces demand for both Good B and its complement Good A (ink cartridges or cinema popcorn). 3. UNRELATED goods have XED = 0.

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5

Price Elasticity of Supply (PES): Short Run vs Long Run

PES measures the responsiveness of quantity supplied to a change in the good's market price: PES = (%ΔQs) ÷ (%ΔP). Because supply curves slope upwards, PES is always positive: PES > 1 is price elastic supply, and 0 < PES < 1 is price inelastic supply. Determinants of PES (PSSST): 1. Production lag / length of the production process (agricultural crops like cocoa or wheat take months/years to grow, making short-run PES highly inelastic); 2. Stocks / inventories and storability (perishable goods like fresh strawberries cannot be stockpiled, so PES is inelastic); 3. Spare capacity (in a recession with idle factories and unemployed workers, PES is elastic; at full capacity, PES is inelastic); 4. Substitutability and mobility of factors of production (how easily land/labour/capital can be switched from making one product to another); 5. Time period (in the momentary/short run, at least one factor of production is fixed so PES is inelastic; in the long run, all factors are variable so PES is elastic).

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6

Incidence of an Indirect Tax and a Subsidy on Diagrams

When the government imposes a specific (per-unit) indirect tax t, the supply curve shifts vertically upwards by t from S₁ to S₂ (or pivots upwards for an ad valorem percentage tax like VAT). The new equilibrium price rises from P₁ to P₂ (by less than the full vertical tax t unless PED = 0 or PES = ∞), and quantity falls from Q₁ to Q₂: Total Tax Revenue = t × Q₂ = (P₂ - P_producer) × Q₂. Consumer incidence (burden) = (P₂ - P₁) × Q₂. Producer incidence (burden) = (P₁ - P_producer) × Q₂. Rule: Whenever |PED| < PES (demand is more inelastic than supply - e.g., cigarettes, petrol, alcohol), consumers bear the majority of the tax burden (and shifting S₁ to S₂ yields large tax revenue for the government, though only a small drop in Q!). Conversely, when a per-unit subsidy s is granted, supply shifts vertically downwards from S₁ to S₂: consumers receive the price reduction benefit (P₁ - P₂) × Q₂ (largest when demand is inelastic), while producers receive the extra revenue benefit (P_producer - P₁) × Q₂.

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1. Q1

   A train operator increases the price of peak-hour commuter tickets from £20 to £25, causing daily ticket sales to fall from 10,000 to 9,000. At the same time, it reduces the price of off-peak leisure tickets from £15 to £12, causing off-peak ticket sales to rise from 4,000 to 6,000. (a) Calculate the Price Elasticity of Demand (PED) for both peak-hour and off-peak tickets. (b) Calculate the change in daily Total Revenue in each market and explain why the train operator's price discrimination strategy succeeded. (6 marks)

   Check Mark Scheme

   Click “Check Mark Scheme” to compare your answer, 1. (a) Peak-hour tickets: %ΔP = [(25 - 20) ÷ 20] × 100 = +25%; %ΔQd = [(9,000 - 10,000) ÷ 10,000] × 100 = -10%; PED_peak = -10% ÷ +25% = -0.40 (price inelastic) [1 mark]. 2. Off-peak tickets: %ΔP = [(12 - 15) ÷ 15] × 100 = -20%; %ΔQd = [(6,000 - 4,000) ÷ 4,000] × 100 = +50%; PED_off-peak = +50% ÷ -20% = -2.50 (price elastic) [1 mark]. 3. (b) Peak-hour Total Revenue change: Initial TR = £20 × 10,000 = £200,000; New TR = £25 × 9,000 = £225,000 (an increase of +£25,000 per day) [1 mark]. 4. Off-peak Total Revenue change: Initial TR = £15 × 4,000 = £60,000; New TR = £12 × 6,000 = £72,000 (an increase of +£12,000 per day) [1 mark]. 5. Economic explanation: Peak commuters have price inelastic demand (-0.40) because they must travel to work at fixed hours with few substitutes, so raising price increases TR [1 mark]. 6. Off-peak leisure travellers have price elastic demand (-2.50) because travel time is flexible and cars/buses are close substitutes, so cutting price causes a more-than-proportionate surge in sales (+50%) that increases TR [1 mark].

2. Q2

   Explain why agricultural primary commodities (such as coffee beans, wheat, and lithium) typically experience extreme price volatility in global markets, using elasticity concepts and a supply-and-demand diagram reasoning. (6 marks)

   Check Mark Scheme

   Click “Check Mark Scheme” to compare your answer, 1. Price Inelastic Demand (|PED| < 1): Primary food and raw material commodities are basic necessities for consumers and essential manufacturing inputs with very few close substitutes, making their demand curve steep (price inelastic) [2 marks]. 2. Price Inelastic Short-Run Supply (PES < 1): Agricultural crops have long growing/harvesting cycles, depend on weather, and perishable foodstuffs cannot easily be stockpiled (while mines take years to build), making the short-run supply curve also very steep (price inelastic) [2 marks]. 3. Amplified Price Swings on a Diagram: When a supply shock occurs (e.g., drought or frost shifting the steep supply curve S₁ to S₂, or a global boom shifting the steep demand curve D₁ to D₂), the intersection of two highly steep (inelastic) curves produces a massive vertical swing in equilibrium price (P₁ to P₂) alongside only a small change in quantity, destabilising farmer incomes and investment [2 marks].

3. Q3

   A government introduces a specific tax of £4 per unit on sugary fizzy drinks. Before the tax, the equilibrium price was £10 per crate and equilibrium quantity was 50 million crates. After the tax, the market price rises to £13 per crate and equilibrium quantity falls to 42 million crates. Calculate: (a) total government tax revenue, (b) the consumer incidence and producer incidence of the tax, and (c) the percentage of the tax burden paid by consumers, explaining what this implies about PED relative to PES. (6 marks)

   Check Mark Scheme

   Click “Check Mark Scheme” to compare your answer, 1. (a) Total Government Tax Revenue = Tax per unit × New Quantity = £4 × 42 million = £168 million [1 mark]. 2. (b) Consumer tax per unit = P₂ - P₁ = £13 - £10 = £3 per unit; Total Consumer Incidence = £3 × 42 million = £126 million [1 mark]. 3. Producer tax per unit = £4 - £3 = £1 per unit (net price received by producers falls from £10 to £9); Total Producer Incidence = £1 × 42 million = £42 million [1 mark]. 4. (c) Percentage of tax burden paid by consumers = (£3 ÷ £4) × 100 = 75% (while producers pay 25%) [1 mark]. 5. Because consumers bear 3 times as much of the tax burden as producers, the Price Elasticity of Demand |PED| must be significantly more inelastic than the Price Elasticity of Supply PES (specifically, |PED| = (8/50)/(3/10) = 0.53 vs PES = (8/50)/(1/10) = 1.60) [2 marks].

4. Q4

   Evaluate the usefulness and limitations of elasticity estimates (PED, YED, and XED) for a supermarket chain planning its pricing and inventory strategy ahead of a predicted economic recession. (7 marks)

   Check Mark Scheme

   Click “Check Mark Scheme” to compare your answer, 1. Using YED in a Recession: As real household incomes fall during a recession, the supermarket should reduce stock of luxury lines with high positive YED (YED > +1, e.g., Finest organic steaks) and expand shelf space and marketing for own-brand 'Value' inferior goods with negative YED (YED < 0), whose demand will rise counter-cyclically [2 marks]. 2. Using PED and XED for Pricing: For staple inelastic necessities (|PED| < 1), margins can be maintained, whereas for products facing fierce competition from discounters like Aldi/Lidl (high positive XED), cutting prices on elastic 'known value items' (loss leaders) attracts price-sensitive shoppers who then buy complementary high-margin goods (negative XED) [2 marks]. 3. Evaluation / Limitations of Elasticity Data: Ceteris Paribus assumption fails in reality: Elasticity formulas assume only one variable changes at a time, whereas in a recession incomes, competitor prices, consumer confidence, and interest rates all change simultaneously [1 mark]. Historical/Sample Inaccuracy: Elasticity figures are estimated from past sales data and quickly become outdated as consumer tastes and inflation shift [1 mark]. Elasticity does not measure Costs: Maximising Total Revenue (where PED = -1) is not the same as maximising Profit (MC = MR), because expanding output after a price cut also increases total variable costs [1 mark].

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